It will be challenging to find someone with experience with the A6500 since it's not yet available. B&H says it will start shipping November 30.
I am a Fuji owner but not a Fuji fanboy. Cameras are tools, complex tools, and to decide between them requires both handling them, eg ergonomics, menus, etc, as well as looking at the quality of the files from the sensor with a "typical" lens, ideally one's most commonly used lens. Lenses cannot realistically be separated from sensors. This is why those cameras with fixed lenses carefully matched to their sensors seem to do so well, eg the Fuji X100 series, the Sony RX1R, and the Sigma DP Merrill's.
You can certainly find examples of files from the Fuji X T-2 and from the Sony 6300 to compare for yourself. Both cameras, being mirrorless with short flange distances, allow the use with adaptors, with varying compromises, of lenses from many manufacturers as well as their own "native" mount lenses. We all pixel peep, even those of us who vehemently deny that we do. I happen to be a sharpness freak, coming from view cameras and high megapixel Nikons before I switched to Fuji. I found that at the sizes I print, from 6x9 to 9x13, to the occasional 13x20, I've been quite happy with what I got from the 16MP Fuji X T-1 and with more time to shoot, process, and print, expect to be even happier with my new 24MP Fuji X T-2. I like Fuji's style and handling and their history of providing improvements via free firmware rather than expensive new bodies. I rented a Sony A7RII a while back to see what I was "missing," and found I was not missing much, so stuck with my Fuji system. The A7RII is a fine camera, make no mistake. The limitations in my photography tend to come from the operator and not often from the equipment, and we're talking about minor variations in excellent equipment in this discussion.
Like any complex system, I suspect isolating just IQ, whatever that really is, will be challenging but go for it and please let us know what you find out. Good luck on your quest, to paraphrase Monty Python and the Holy Grrrrail.